a_106_Nqueen_oneSolution.java

public class a_106_Nqueen_oneSolution {
    public static boolean isSafe(char chess[][], int row, int col){
        // verticals up 
        for(int i = row-1 ; i>=0 ; i--){
            if(chess[i][col] == 'Q'){
                return false ;
            }
        }

        // left diagonal 
        for(int i=row-1, j=col-1 ; i>=0 && j>=0; i--, j--){
            if(chess[i][j] == 'Q'){
                return false;
            }
        }

        // right diagonal
        for(int i=row-1, j=col+1 ; i>=0 && j<chess.length; i--, j++){
            if(chess[i][j] == 'Q'){
                return false;
            }
    }
    return true ;
}
    public static boolean nQueen(char chess[][], int row){
        // base case
        if(row == chess.length) {
            return true;
        }
        
        // colums loop 
        for(int j=0; j<chess.length; j++){
            if(isSafe(chess,row,j) ){
                chess[row][j] = 'Q' ;         
                if( nQueen(chess, row+1) ) {
                    return true ;
                }     
                chess[row][j] = 'x' ;       // backtracking step 
            }
        }
      return false ;
    }

    public static void printchess(char chess[][]){
        System.out.println("------chess board------");
        
        for(int i=0; i<chess.length; i++){
            for(int j=0; j<chess.length ; j++){
                System.out.print(chess[i][j] + " ");
            }
            System.out.println();
        }

    }

    public static void main(String[] args) {
        int n = 9 ;
        char chess[][] = new char[n][n] ;

        // initialize
        for(int i=0; i<n; i++){
            for(int j=0; j<n; j++){
                chess[i][j]  = 'x' ;
            }
        }

       if( nQueen(chess, 0) ){
        System.out.println("Solution are possible");
        printchess(chess);
       }
       else{
        System.out.println("Solution are Not possible");
       }
        

    }
}